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Review
. 2014 Oct 1;3(5):233-41.
doi: 10.1089/biores.2014.0024.

Mathematical Modeling of HIV Dynamics After Antiretroviral Therapy Initiation: A Review

Pablo S Rivadeneira  1 , Claude H Moog  2 , Guy-Bart Stan  3 , Cecile Brunet  4 , François Raffi  4 , Virginie Ferré  4 , Vicente Costanza  5 , Marie J Mhawej  2 , Federico Biafore  6 , Djomangan A Ouattara  2 , Damien Ernst  7 , Raphael Fonteneau  7 , Xiaohua Xia  8
Affiliations
Review

Mathematical Modeling of HIV Dynamics After Antiretroviral Therapy Initiation: A Review

Pablo S Rivadeneira et al. Biores Open Access. .

Abstract

This review shows the potential ground-breaking impact that mathematical tools may have in the analysis and the understanding of the HIV dynamics. In the first part, early diagnosis of immunological failure is inferred from the estimation of certain parameters of a mathematical model of the HIV infection dynamics. This method is supported by clinical research results from an original clinical trial: data just after 1 month following therapy initiation are used to carry out the model identification. The diagnosis is shown to be consistent with results from monitoring of the patients after 6 months. In the second part of this review, prospective research results are given for the design of individual anti-HIV treatments optimizing the recovery of the immune system and minimizing side effects. In this respect, two methods are discussed. The first one combines HIV population dynamics with pharmacokinetics and pharmacodynamics models to generate drug treatments using impulsive control systems. The second one is based on optimal control theory and uses a recently published differential equation to model the side effects produced by highly active antiretroviral therapy therapies. The main advantage of these revisited methods is that the drug treatment is computed directly in amounts of drugs, which is easier to interpret by physicians and patients.

Keywords: AIDS; HIV; aid for diagnosis; apoptosis; dynamical systems; modeling; nonlinear control; pharmacodynamics; pharmacokinetics.

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Figures

<b>FIG. 1.</b>
FIG. 1.
Viral load time evolution for four patients. The samples are taken frequently at the beginning of the trial.
<b>FIG. 2.</b>
FIG. 2.
(a) Time evolution of HIV infection during zidovudine (ZDV) monotherapy is depicted on the left side. (b) The doses, administrated twice a day, are computed by means of a feedback linearizing impulsive control; their amplitude is drawn on the right side.
<b>FIG. 3.</b>
FIG. 3.
Comparison between optimal V virus trajectories for medications that take or do not take side effects into account, controlled by the weight parameter a4 in the cost function J(u).
<b>FIG. 4.</b>
FIG. 4.
Optimal control strategies for different decisions regarding the cost weight a4.
<b>FIG. 5.</b>
FIG. 5.
Optimal evolution of side effects for different decisions regarding the cost weight a4.
See this image and copyright information in PMC

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